According to special relativity, an observer cannot move away from or towards a light source at the speed of light, denoted as c. The speed of light is an absolute constant in vacuum, and it is the same for all inertial observers, regardless of their relative motion.
The theory of relativity states that the speed of light in a vacuum is always measured to be c, approximately 299,792,458 meters per second, regardless of the motion of the source or the observer. This is a fundamental postulate of special relativity and has been experimentally verified.
In the scenario you described, if an observer were somehow able to move at the speed of light relative to a light source, two important consequences arise:
Time dilation: According to special relativity, as an object approaches the speed of light, time dilation occurs. This means that time would appear to slow down for the moving observer relative to a stationary observer. However, as an object approaches the speed of light, the time dilation becomes more pronounced, eventually becoming infinite as the object's velocity reaches c. Therefore, from the perspective of the observer moving at the speed of light, time would not progress.
Mass increase: As an object accelerates and approaches the speed of light, its relativistic mass increases. This effect is described by Einstein's mass-energy equivalence principle (E=mc²). As an object's speed approaches c, its mass increases to infinity. Consequently, it would require an infinite amount of energy to accelerate a massive object to the speed of light.
In summary, according to special relativity, an observer cannot move away from or towards a light source at the speed of light. The speed of light is an absolute constant, and the theory predicts that time dilation and mass increase would occur as an object approaches the speed of light, making it impossible to reach or exceed this speed.